What is the arc length of the curve given by f ( x ) = 1 + cos &#x2061;<!-- ⁡ -->

Keenan Santos

Keenan Santos

Answered question

2022-07-12

What is the arc length of the curve given by f ( x ) = 1 + cos x in the interval x [ 0 , 2 π ]?

Answer & Explanation

Tristin Case

Tristin Case

Beginner2022-07-13Added 15 answers

Recall that arc length is given by A = a b 1 + ( d y d x ) 2 d x
The derivative of f'(x) is f ( x ) = sin x
A = 0 2 π 1 + ( sin x ) 2 d x
A = 0 2 π 1 + sin 2 x
An approximation using a calculator gives A=7.64

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